How many sequences contain exactly three heads when you flip a coin five times? my answer was 15 but apparently I am wrong
2
15
10
8
12
HHHTT
HTHHT
HTTHH
HHTHT
HHTTH
HTHTH
TTHHH
THTHH
THHTH
THHHT
Can you think of any other sequences?
httth
To determine the number of sequences that contain exactly three heads when you flip a coin five times, you can use the concept of combinations.
When you flip a coin, there are two possible outcomes: heads or tails. So, for each flip, there are two possibilities. Since you are flipping the coin five times, there are a total of 2 * 2 * 2 * 2 * 2 = 32 possible sequences.
To count the number of sequences that contain exactly three heads, you can use the formula for combinations, which is nCr = n! / (r! * (n - r)!). In this case, n (the total number of flips) is 5, and r (the number of heads) is 3.
Using the formula, the number of sequences with three heads can be calculated as follows:
1. Calculate n! (n factorial): n! = 5 * 4 * 3 * 2 * 1 = 120.
2. Calculate r! ((n - r)! factorial): r! = (5 - 3)! = 2! = 2.
3. Calculate (n - r)! ((n - r)! factorial): (n - r)! = (5 - 3)! = 2! = 2.
4. Plug the values from steps 1, 2, and 3 into the formula: 120 / (2 * 2) = 120 / 4 = 30.
Therefore, the correct answer is 30 sequences that contain exactly three heads when you flip a coin five times, not 15.